Spatiotemporal control of structure and dynamics in a polar active fluid

TL;DR

This paper develops optimal control strategies for polar active fluids, enabling targeted manipulation of their emergent behaviors such as relocating structures and switching dynamical states, with implications for experimental and engineering applications.

Contribution

It introduces a novel application of optimal control theory to polar active fluids, demonstrating precise manipulation of their structure and dynamics using external actuation.

Findings

Control protocols can relocate asters to specific locations.

Propagating waves can be reoriented in desired directions.

Switching between stationary and propagating states is achievable.

Abstract

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.